Fuzzy Probabilistic Sets and r-Fuzzy Sets

Author

Yuan, Xue-hai ; Li, Hong-xing ; Zhang, Cheng

Author_Institution

Sch. of Electron. & Inf. Eng., Dalian Univ. of Technol., Dalian

Volume

1

fYear

2008

fDate

18-20 Oct. 2008

Firstpage

271

Lastpage

276

Abstract

In this paper, a connection between the fuzzy probabilistic set and the r-fuzzy set is established. Firstly, a new concept of r-fuzzy nested set is presented and it is pointed that a fuzzy probabilistic set is an equivalent class of a r-fuzzy nested set. Secondly, the concepts of fuzzy probabilistic subgroup and r-fuzzy subgroup of a group are given respectively, the relations between fuzzy probabilistic subgroups and fuzzy subgroups presented by Rosenfeld and the properties of r-fuzzy subgroups are discussed. Finally, the membership function of fuzzy probabilistic sets and r-fuzzy subgroups are defined, the properties of membership function of r-fuzzy subgroups are studied.

Keywords

fuzzy set theory; group theory; fuzzy membership function; fuzzy probabilistic sets; fuzzy probabilistic subgroup; r-fuzzy nested set; r-fuzzy subgroup; Control theory; Fuzzy logic; Fuzzy sets; Fuzzy systems; Image processing; Knowledge engineering; Mathematics; Pattern recognition; Random variables; Topology; fuzzy probabilistic set; fuzzy probabilistic subgroup; r-fuzzy nested set; r-fuzzy set; r-fuzzy subgroup;

fLanguage

English

Publisher

ieee

Conference_Titel

Fuzzy Systems and Knowledge Discovery, 2008. FSKD '08. Fifth International Conference on

Conference_Location

Shandong

Print_ISBN

978-0-7695-3305-6

Type

conf

DOI

10.1109/FSKD.2008.100

Filename

4665982